On many occasions Jobst Brandt has
written about a tire bead test. Recently:

"[T]he tires we ride are in
fact clinchers that stay on the rim primarily by the
clinch of the hooked sidewall that retains the tire bead.
To test this, I cut the bead wire in five places (on a
tire that was worn out) and mounted it on an Mavic MA-2
rim where it stayed in place while inflating it to 100
psi."

For fun, a friend and I replicated this
test, with photos below. An old worn out Specialized
Armadillo from my tandem was a good candidate tire.

We cut both beads in five
places around the circumference.

You can see the steel bead is
in fact cut through. We then mounted the tire with an
inner tube onto a good used Velocity Aerohead rim.

The mounted tire was a
shockingly loose fit on the rim. The handle of the
diagonal cutters easily slipped fully between the rim
and both beads of the tire with its larger dimension
vertical.

We carefully inflated the
tire. Even though we were wearing leather gloves,
long pants, ear and eye protection, I chickened out
after we reached about 110 psi. Result: The tire did
not blow off the rim despite the cut bead making a
tight fit impossible.

Conclusion: Clincher tires stay on the
rim primarily by the clinch of the hooked sidewall that
retains the tire bead, not the circumferential tension in the
bead. What this means is that a tire does not need a tight
fit for it to stay on the rim; it needs a rim with a hooked
sidewall, and air in the tire.